202 ANALYTICAL MECHANICS 12. Find the power lost due to friction in the bearings of a water turbine under the following conditions: The rotating system, which weighs 50 tons, is supported by a flat-end pivot bearing 10 inches in diameter. The coefficient of friction is 0.01. The turbine makes 250 revolutions per minute. . 13. In the preceding problem suppose the shaft which carries the rotating system to be hollow, with an inner diameter of 6 inches and outer diameter of 12 inches. 14. In problem 12 suppose the bearing to be a hemispherical pivot with constant normal pressure. 15. In the preceding problem suppose the vertical component of the normal pressure to be constant.